Entire Scalar Curvature Flow and Hypersurfaces of Constant Scalar Curvature in Minkowski Space

We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacelike hypersurface with constant scalar curvature. The proofs rely on barriers construction and a priori estimates.

Keywords

Entire graphs, prescribed scalar curvature, scalar curvature flow, Minkowski space

2010 Mathematics Subject Classification

35J60, 35K55, 53C50

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Published 1 January 2009